The Mathematics of Elegance Knotting Your Tie by Federico Peiretti
	Mathematics and fashion, decidedly an unusual combination, has produced some results that could very well change our daily habits, things we do every morning without thinking, like knotting our ties or tying our shoes. This strange research comes from two English physicists at Cambridge University, Thomas Fink and Yong Mao, who were able to establish that the number of possible ways to knot a tie is 85 (until now, only four ways have been commonly used). The oldest tie knot, started in England at the end of the 1800's, is called the "Four in Hand", used originally by coachmen to tie scarves around their necks. Another two famous knots, the "Windsor" and the "Half-Windsor", became popular during the 1930's as the personal style of the Duke of Windsor. The last knot, the "Pratt", has gained popularity only in the last decade. Fink and Mao (whose scientific specialty is the study of proteins) decided that we shouldn't have to wait another 50 years for the discovery of a new tie knot, since with mathematics the question can be resolved once and for all. For this reason, they created a mathematical model to simulate the various steps used in constructing a knot, which was then presented in the prestigious scientific magazine, Nature (Mar 4, 1999). Their biggest difficulty, according to Dr. Fink, was figuring out how to represent esthetic criteria using mathematical terms. Tying a knot always starts by using the tip of the wider part of the tie, that is then brought over or under the tip of the narrower part, and continues with a series of movements, half-turns, that rotate the wider tip to the left, center, and right, over or under the narrower tip, toward the "inside", that is, toward the shirt or away from the shirt. Using this reasoning they reached the key finding of the study: a mathematical model based on a triangular grid system, on which a succession of random movements happen. These movements are techincally called a "random walk". They established a maximum of nine possible movements, with the further restriction that not more than two successive movements can be made in the same direction. From this, Fink and Mao arrived at the final number of 85 possible tie knots, including the four well known classic ones. From these 85 possibilities, the scientists then selected six "finalists", new knots which they saw as the most promising based on both their attractive symmetric qualities and the ease of movements needed to make them. The six newly-discovered knots don't have names yet; for now they're identified simply by a pair of numbers. The first number indicates the total number of movements required (excluding the final movement to close the knot). The second indicates the number of "key" movements. One of the best-looking, the (7,2), has already been approved by the most prestigious fashion house in London, Gieves and Hawkes (Prince Charles' personal tailors), who have baptized it "The "Fink".